U.S. Provisional Application 60/822,028 filed on Aug. 10, 2006 and co-pending patent application describe an oven capable of cooking foods at accelerated times compared to conventional ovens.
Specifically, the oven described consists of a stored energy system, a switching system, a food holder, and radiant heat bulbs used to cook the food. Typical cook times (in seconds) for a system running about 20 KW of power are described below:
Thin Slice Toast (white bread)3.5Bagel Half (plain)5Hog Dog (directly from refrigerator)20Pizza (directly from freezer)22Bacon Strips (grilled in fat)30-40Grilled Cheese Sandwich10-15
The radiant heat bulbs are central to the prior art as they produce the appropriate wavelength of infrared energy required (in the range of 1 to 3 nanometers) and the multiple bulbs provide the intensity. Typical bulbs include halogen based bulbs similar to those produced by companies such as Ushio, Sylvania, or Soneko with power density of approximately 100 w/in2. Although these bulbs are effective at reducing cook times, they have several primary draw backs which have to this point deterred the prior art from successful introduction in the marketplace. Specifically;    1) The price for bulbs is high relative to the entire price required to commercialize a unit such as a toaster.    2) Bulbs can easily get damaged by oils and grease common in the cooking process.    3) Use of glass shielding over the bulbs decreases the intensity of the radiant energy.    4) Although fewer, longer, high voltage bulbs can be used, the voltage poses safety risks and therefore, low voltages are preferable. Unfortunately though, the use of smaller bulbs further requires that many bulbs be used; complicating manufacturing and overall pricing issues.
Another method for heating involves the use of Nichrome wire. Nichrome wire is commonly used in appliances such as hair dryers and toasters as well as used in embedded ceramic heaters. The wire has a high tensile strength and can easily operate at temperatures as high as 1250 degrees Celsius.
Nichrome has the following physical properties:
Material propertyValueUnitsTensile Strength2.8 × 108 PaModulus of elasticity2.2 × 1011PaSpecific gravity   8.4NoneDensity8400kg/m3Melting point1400° C.Electrical resistivity 1.08 × 10−6[1]Ω · mat room temperatureSpecific heat 450J/kg° C.Thermal conductivity   11.3W/m/° C.Thermal expansion 14 × 10−6m/m/° C.Standard ambient temperature and pressure used unless otherwise noted.
When considering the use of Nichrome within an oven it is important to consider not only the resistive characteristics but also the black body emission of the element when hot.
With regard to the general characterization of resistive elements,
The resistance is proportional to the length and resistivity, and inversely proportional to the area of the conductor.
                    R        =                                            L              A                        ·            ρ                    =                                    L              A                        ·                                          ρ                0                            ⁡                              (                                                      α                    ⁡                                          (                                              T                        -                                                  T                          0                                                                    )                                                        +                  1                                )                                                                        Eq        .                                  ⁢        1            where ρ is the resistivity:
      ρ    =          1      σ        ;
L is the length of the conductor, A is its cross-sectional area, T is its temperature, T0 is a reference temperature (usually room temperature), ρ0 is the resistivity at T0, and α is the change in resistivity per unit of temperature as a percentage of ρ0. In the above expression, it is assumed that L and A remain unchanged within the temperature range. Also note that ρ0 and α are constants that depend on the conductor being considered. For Nichrome, ρ0 is the resistivity at 20 degrees C. or 1.10×10−6 and α=0.0004. From above, the increase in radius of a resistive element by a factor of two will decrease the resistance by a factor of four; the converse is also true.
Regarding the power dissipated from a resistive element, where, I is the current and R is the resistance in ohms, v is the voltage across the element, from Ohm's law it can be seen that, since v=iR,P=i2R
In the case of an element with a constant voltage electrical source, such as a battery, the current passing through the element is a function of its resistance. Replacing R from above, and using ohms law,P=v2/R=v2A/ρ0L  Eq. 2
In the case of a resistive element such as a nichrome wire the heat generated within the element quickly dissipates as radiation cooling the entire element.
Now, considering the blackbody characterization of the element:
Assuming the element behaves as a blackbody, the Stefan-Boltzmann equation characterizes the power dissipated as radiation:W=σ·A·T4  Eq. 3
Further, the wavelength λ, for which the emission intensity is highest, is given by Wien's Law as:
                              λ          max                =                  b          T                                    Eq        .                                  ⁢        4            Where,                σ is the Stefan-Boltzmann constant of 5.670×10−8 W·m−2·K−4 and,        b is the Wien's displacement constant of 2.897×10−3 m·K.        
In an application such as a cooking oven, requiring a preferred operating wavelength of 2 microns (2×10E−6) for maximum efficiency, the temperature of the element based on Wein's Law should approach 1400 degrees K or 1127 degrees C. From the Stefan-Boltzmann equation, a small oven with two heating sides would have an operating surface area of approximately 4×0.25 m×0.25 m or 0.25 m2. Thus, W should approach 20,000 Watts for the oven.
In the case of creating a safe high power toaster or oven it is necessary for the system to operate at a low voltage of no more than 24 volts. Thus, using Eq. 2 with 20,000 W, the element will have a resistance of approximately 0.041 ohms, if 100% efficient at the operating temperature. Based on Eq. 1, a decrease in operating temperature to room temperature (from 1400 to 293 k) represents an approximate decrease in the resistivity of the element by about 1.44 times, and therefore an element whose resistance at room temperature is 0.0284 ohms is required.
Now, considering the relationship of the resistance of the element and the characterization of the element as a blackbody:
The ratio of the resistance of the heater to the black body raditive area of the same heater becomes the critical design constraint for the oven; herein termed the De Luca Element Ratio. The ideal oven for foods operating over a 0.25 square meter area at 2 micron wavelength has a De Luca Element Ratio (at room temperature), of 0.1137 ohms/m2 (0.0284 ohms/0.25 m2). The De Luca Element Ratio is dependant solely on the resistance of the material and the radiative surface area but is independent of the voltage the system is operated. In addition, for wire, the length of the wire will not change the ratio.
Table 1 lists the resistance per meter of several common nichrome wire sizes as well as the De Luca Element Ratio for these elements. It is important to note that all these wires have a De Luca Element Ratio far greater than the 0.1137 required for an oven operated at 1400K, 24V, and over 0.25 m2. Clearly the use of a single wire with a voltage placed from end-to-end in order to achieve the power requirement is not feasible.
In contrast, a household pop-toaster, operated at 120V and 1500 W, over a smaller 0.338 m2 area at 500K would require a De Luca Element Ratio of 35.5. Thus a 1 meter nichrome wire of 0.001 m radius with a 120V placed across it would work appropriately.
TABLE 1SurfaceDe LucaTimeResistanceArea ofElementTo ReachWireCrossPer Meter1 meterRatio1400KRadiusSectionalLengthlengthWeight Per(at roomAt 20 kw(m)Area (m2)(ohms)(m2)Meter (g)temp)(sec)0.013.14E−040.00340.062826370.165.40.00157.06E−060.150.0094259.316.21.470.0013.14E−060.30.0062826.347.70.654.00057.85E−071.38.003146.64380.1630.0001911.139E−07 11.600.001200.95796700.0240.0001275.064E−08 24.610.000790.425308560.0100.0000221.551E−09 771.210.0001380.01355804860.0003
Clearly a lower resistance or a higher surface area is required to achieve a De Luca Element Ratio of close to 0.1137.
One way to achieve the De Luca Ratio of 0.1137 would be to use a large element of 2 cm radius. The problem with this relates to the inherent heat capacity of the element. Note from Table 1 that to raise the temperature to 1400K from room temperature would require 65.4 seconds and thus about 0.36 KWH of energy.
This calculation is derived from the equation relating heat energy to specific heat capacity, where the unit quantity is in terms of mass is:ΔQ=mcΔTwhere ΔQ is the heat energy put into or taken out of the element (where P×time=ΔQ), m is the mass of the element, c is the specific heat capacity, and ΔT is the temperature differential where the initial temperature is subtracted from the final temperature.
Thus, the time required to heat the element would be extraordinarily long and not achieve the goal of quick cooking times.
Another way for lowering the resistance is to place multiple resistors in parallel. Kirkoff's law's predict the cumulative result of resistors placed in parallel.

                              1                      R            total                          =                              1                          R              1                                +                      1                          R              2                                +          …          +                      1                          R              n                                                          Eq        .                                  ⁢        5            
The following Table 2 lists the number of conductors for each of the elements in Table 1, as derived using equation 5, that would need to be placed in parallel in order to achieve a De Luca Element Ratio of 0.1137. Clearly placing and distributing these elements evenly across the surface would be extremely difficult and impossible for manufacture. Also note that the required time to heat the combined mass of the elements to 1400K from room temperature at 20 KW for elements with a radius of greater than 0.0002 meters is too large with respect to an overall cooking time of several seconds.
TABLE 2Number ofDe LucaParallelTime ToElementElementsReachRatio forRequired to1400 KWiresingleAchieveTotalAt 20 kwRadiuselement (@De Luca RatioWeight/(sec) From(m)Room Temp)of 0.1137Meter (g)Room Temp0.010.11263765.40.001516.21271117.60.00147.72257914.4.00054386341510.30.00019196702672556.30.000127308564932095.20.00002255804866838882.18